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3 years ago

Which statement are true about the angles in the diagram? Check all that apply

Mathematics

2 answers:

katrin [286]3 years ago

7 0

Answer:

the last one

Step-by-step explanation:

angle bcd is congrulent to ace

Ivanshal [37]3 years ago

7 0

Answer:

Options B,C,E are true.

Step-by-step explanation:

It has been given in the question ∠ACD is supplementary to ∠ACE and ∠BCD

∠ACD ≅ ∠BCE

Option A. ∠ACE is supplementary to ∠BCD

False. They are not lying on a point of straight line.

∠ACE + ∠BCD ≠180°

Option B. ∠BCE is supplementary to ∠ACE

Since ∠ACD + ∠ACE = 180° [Given]

and ∠ACD ≅ ∠BCE [Given]

Therefore, ∠BCE + ∠ACE = 180°

TRUE.

Option C. ∠BCD is supplementary to ∠BCE

Since ∠ACD + ∠BCD = 180°[Given]

and ∠ACD ≅ ∠BCE [Given]

So ∠BCE + ∠BCD = 180°

TRUE.

Option D. ∠ACE ≅ ∠BCE

Since ∠ACD + ∠ACE = 180°

And ∠ACD + ∠BCD = 180°

This is clear from these equations that ∠ACE is supplementary to ∠BCD.

FALSE :

Option E. ∠BCD is congruent to ∠ACE

As we have already proved in option D. ∠BCD ≅ ∠ACE

TRUE

Therefore, Options B, C, E are TRUE

You might be interested in

Find the Area. Simplify your answer.

Vaselesa [24]

Answer:

Area = $9x^2$ square units

Step-by-step explanation:

Key skills needed: Area of a parallelogram

1) This shape is a parallelogram, and the way to find the area of a parallelogram is:

$A = bh$

A = area

b = base (the side at the bottom

h = the height ( the length that runs from one side to another and makes a right angle)

2) The base (b) would be 3x. The height (h) would also be 3x

3) This means A = $3x(3x)$

3 times 3 is 9 --> and x times x is $x^2$

Therefore the area is --> $9x^2$

Hope you understood and have a nice day!! :D

5 0

3 years ago

a group raised $276 for its favorite charity. this is 23% of the amount it hopes to raise. how much money does the group want to

OverLord2011 [107]

Answer: The group wants to raise $1,200.

Step-by-step explanation:

We can use a proportion to solve.

part/whole = percent/100

If we insert the values:

276/x = 23/100

We can cross multiply.

276 x 100 = 27,600

27,600 / 23 = 1,200

$1,200 is the answer.

6 0

2 years ago

First make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) x

e-lub [12.9K]

Answer:

$(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

$\int x ln(5+x)dx$

so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:

U=5+x

du=dx

x=U-5

so when substituting the integral will look like this:

$\int (U-5) ln(U)dU$

now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:

$\int (pq')=pq-\int qp'$

so we must define p, q, p' and q':

p=ln U

$p'=\frac{1}{U}dU$

$q=\frac{U^{2}}{2}-5U$

q'=U-5

and now we plug these into the formula:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int \frac{\frac{U^{2}}{2}-5U}{U}dU$

Which simplifies to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int (\frac{U}{2}-5)dU$

Which solves to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\frac{U^{2}}{4}+5U+C$

so we can substitute U back, so we get:

$\int xln(x+5)dU=(\frac{(x+5)^{2}}{2}-5(x+5))ln(x+5)-\frac{(x+5)^{2}}{4}+5(x+5)+C$

and now we can simplify:

$\int xln(x+5)dU=(\frac{x^{2}}{2}+5x+\frac{25}{2}-25-5x)ln(5+x)-\frac{x^{2}+10x+25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}-\frac{5x}{2}-\frac{25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

notice how all the constants were combined into one big constant C.

7 0

3 years ago

Can you factor -2x + 6 to get -2(x - 3)

QveST [7]

Answer:

Yes

Step-by-step explanation:

Divide -2x + 6 by -2, then bring the -2 outside the bracket

6 0

3 years ago

A cylindrical tank lying on its side is filled with liquid weighing 50lb/ft^3. Find the work required to pump all the liquid to

nikklg [1K]

You can use the fact that the work done is equivalent to finding the center of mass of the water in the tank(which is at the center of the cylindrical cross section, which is 3 ft below the level to which the liquid is pumped. Call this distance h.
You then need the total mass of the liquid, volume X density=m. This is where pi comes in!
Work needed =mgh, where g is the gravitational acceleration.

4 0

3 years ago